A326143 a(n) = A326142(n) - n, where A326142 gives the sum of all other divisors of n except its largest squarefree divisor.

-1, -1, -2, 1, -4, 0, -6, 5, 1, -2, -10, 10, -12, -4, -6, 13, -16, 15, -18, 12, -10, -8, -22, 30, 1, -10, 10, 14, -28, 12, -30, 29, -18, -14, -22, 49, -36, -16, -22, 40, -40, 12, -42, 18, 18, -20, -46, 70, 1, 33, -30, 20, -52, 60, -38, 50, -34, -26, -58, 78, -60, -28, 20, 61, -46, 12, -66, 24, -42, 4, -70, 117, -72, -34, 34, 26, -58, 12

Offset: 1

Author

Antti Karttunen, Jun 09 2019

Keywords

• sign
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A001065, A007947, A033879, A066503, A326142, A326144.

Cf. also A326054, A326127.

Cf. A013661, A065463.

Programs

Mathematica

rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; a[n_] := DivisorSigma[1, n] - rad[n] - n; Array[a, 100] (* Amiram Eldar, Dec 05 2023 *)

PARI

A007947(n) = factorback(factorint(n)[, 1]);
A326143(n) = (sigma(n)-A007947(n)-n);

Formula

a(n) = A326142(n) - n = (A000203(n)-A007947(n)) - n = A001065(n) - A007947(n).

a(n) = A066503(n) - A033879(n).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A013661 - A065463 - 1 = -0.0595081... . - Amiram Eldar, Dec 05 2023